one linearly independent vector to span a line, two linearly independent vectors to span a plane, and 3 linearly independent vectors to span a 3-dimensional space, and so forth any n vectors that span an n-dimensional space are going to be linearly independent. So i see I'm going to have 2...
I was trying to say that the vectors {-3,0,1} and {5,1,0} form the basis for the nullspace of A and that I'm not seeing how to give a geometric description of the nullspace of A.
i found that a0=0, then a2=t, and a1=-t those are the three linearly independent solutions, so what i thought the basis would look like in vector form would bex € P2 such that x=t(0,-1,1)
W=p(x)={a0 + a1x + a2x2}
so I'm not sure if this is right but I'm trying to work through it, so since the set W is a set of polynomials in P2 then p(x)={a0+a1 +a2} and a0 would be zero since p(1)=0. Then therefore the basis for W would be = (0,-1,1) but i think the dim(W) is 2-dimensional but...
Homework Statement
general form of solutions to Ax=b
Consider matrix A=
{[ 2 -10 6 ]
[ 4 -20 12 ]
[ 1 -5 3 ]}
Find a basis for the nullspace of A. Give a geometric description of the nullspace of A.
The Attempt at a Solution
I found the...
I'm trying to show that a set W of polynomials in P2 such that p(1)=0 is a subspace of P2. Then find a basis for W and dim(W).
I have already found that the set W is a subspace of P2 because it is closed under addition and scalar multiplication and have showed that. The thing I'm stuck on...